There is well known a vehicular drive system provided with a step-variable transmission portion which is shifted to a selected one of a plurality of speed positions having respective speed ratio values, with engaging and releasing actions of a plurality of coupling devices, and a drive power source portion operatively connected to an input shaft of the step-variable transmission portion in a power transmittable manner. JP-2012-46003A discloses an example of this type of vehicular drive system (vehicular power transmitting system). This publication describes an adequate progress of a shift-down action of the step-variable transmission portion in a coasting run of a vehicle (coasting shift-down action), by raising a rotating speed of the input shaft of the step-variable transmission portion from a pre-shift-down synchronizing speed to a post-shift-down synchronizing speed, with an input shaft torque transmitted from the drive power source portion to the input shaft. The publication also describes that a rate of increase of the input shaft torque is reduced with a decrease of a temperature of a working fluid supplied to the coupling devices, and a moment of initiation of a change of the input shaft torque is delayed with the decrease of the temperature.
By the way, each of the coupling devices of the step-variable transmission portion includes friction plates which are rotated relative to each other, and a lubricant is supplied between the adjacent friction plates. The relative rotary motions of the friction plates cause a dragging loss due to the lubricant existing between the adjacent friction plates, even when the coupling device is placed in its released state. This dragging loss (dragging torque) in the step-variable transmission portion due to the lubricant increases with a decrease of the temperature of the lubricant, so that the input shaft speed of the step-variable transmission portion cannot be raised to the post-shift-down synchronizing speed if the value of the torque transmitted to the input shaft of the step-variable transmission portion during the coasting shift-down action when the lubricant temperature is comparatively low is the same as that when the lubricant temperature is normal. In this case, the coasting shift-down action of the step-variable transmission portion does not adequately progress, or takes place in a reverse direction, giving rise to a problem of generation of a shifting shock of the step-variable transmission portion and consequent deterioration of drivability of the vehicle.